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system of equations \sum_{i=1}^{n} x_i^k= a^k

Source: Austrian Polish 1979 APMC

April 26, 2020
algebrasystem of equations

Problem Statement

A positive integer nn and a real number aa are given. Find all nn-tuples (x1,...,xn)(x_1, ... ,x_n) of real numbers that satisfy the system of equations ∑i=1nxik=ak    for    k=1,2,...,n\sum_{i=1}^{n} x_i^k= a^k \,\,\,\, for \,\,\,\, k = 1,2, ... ,n
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